scholarly journals Numerical dissipation of flux splitting schemes for contact discontinuities

2021 ◽  
Author(s):  
Jun Liu ◽  
Fang Han ◽  
Yan Xin Wei
Keyword(s):  
Contact Discontinuity ◽  
High Order Accuracy ◽  
Numerical Dissipation ◽  
Splitting Schemes ◽  
Flux Splitting ◽  
Low Dissipation ◽  
Contact Discontinuities ◽  
Two Dimensional Flow ◽  
Discontinuity Problem ◽  
Accuracy Difference

Abstract The contact discontinuity is simulated by three kinds of flux splitting schemes to evaluate and analyse the influence of numerical dissipation in this paper. The numerical results of one-dimensional contact discontinuity problem show that if the flow velocity on both sides of the contact discontinuity is not simultaneously supersonic, the non-physical pressure and velocity waves may occur when the initial theoretically contact discontinuity is smeared into a transition zone spanning several grid-cells caused by numerical dissipations. Since these non-physical waves have no effect on the corresponding density dissipation, this paper considers these fluctuations as only numerical errors and are not part of the numerical dissipation. In addition, for two-dimensional flow field, the characteristics of high-order accuracy difference schemes, i.e. low dissipation and high resolution, may induce the multi-dimensional non-physical waves that interfere with each other to produce more complex non-physical flow structures, so the fluctuations in the calculated results should be treated with caution.

scholarly journals Collision of merger and accretion shocks: formation of Mpc-scale contact discontinuity in the Perseus cluster

2020 ◽  
Vol 498 (1) ◽  
pp. L130-L134
Author(s):  
Congyao Zhang ◽  
Eugene Churazov ◽  
Klaus Dolag ◽  
William R Forman ◽  
Irina Zhuravleva
Keyword(s):  
Contact Discontinuity ◽  
Alternative Scenario ◽  
X Ray ◽  
Cold Fronts ◽  
Contact Discontinuities ◽  
Accretion Shock ◽  
Perseus Cluster ◽  
Accretion Shocks

ABSTRACT Two Mpc-size contact discontinuities have recently been identified in the XMM–Newton and Suzaku X-ray observations in the outskirts of the Perseus cluster (Walker et al.). These structures have been tentatively interpreted as ‘sloshing cold fronts’, which are customarily associated with differential motions of the cluster gas, perturbed by a merger. In this study, we consider an alternative scenario, namely, that the most prominent discontinuity, near the cluster virial radius, is the result of the collision between the accretion shock and a ‘runaway’ merger shock. We also discuss the possible origin of the second discontinuity at ${\sim}1.2{\rm \, Mpc}$.

A novel flux splitting scheme with robustness and low dissipation for hypersonic heating prediction

2018 ◽  
Vol 127 ◽  
pp. 126-137 ◽  
Author(s):  
Shu-sheng Chen ◽  
Chao Yan ◽  
Kang Zhong ◽  
Hai-chao Xue ◽  
Er-long Li
Keyword(s):  
Splitting Scheme ◽  
Flux Splitting ◽  
Low Dissipation

A Non-Local Convective Flux Limiter for Upwind-Biased Finite Volume Simulations

2010 ◽  
Author(s):  
Nicole M. W. Poe ◽  
D. Keith Walters
Keyword(s):  
Finite Volume ◽  
Finite Volume Methods ◽  
Second Order ◽  
Numerical Dissipation ◽  
Ansys Fluent ◽  
First Order ◽  
Low Dissipation ◽  
Solution Convergence ◽  
Improve Accuracy ◽  
Non Local

Finite volume methods on structured and unstructured meshes often utilize second-order, upwind-biased linear reconstruction schemes to approximate the convective terms, in an attempt to improve accuracy over first-order methods. Limiters are employed to reduce the inherent variable over- and under-shoot of these schemes; however, they also can significantly increase the numerical dissipation of a solution. This paper presents a novel non-local, non-monotonic (NLNM) limiter developed by enforcing cell minima and maxima on dependent variable values projected to cell faces. The minimum and maximum values for a cell are determined primarily through the recursive reference to the minimum and maximum values of its upwind neighbors. The new limiter is implemented using the User Defined Function capability available in the commercial CFD solver Ansys FLUENT. Various simple test cases are presented which exhibit the NLNM limiter’s ability to eliminate non-physical oscillations while maintaining relatively low dissipation of the solution. Results from the new limiter are compared with those from other limited and unlimited second-order upwind (SOU) and first-order upwind (FOU) schemes. For the cases examined in the study, the NLNM limiter was found to improve accuracy without significantly increasing solution convergence rate.

Runge-Kutta Discontinuous Galerkin Method with a Simple and Compact Hermite WENO Limiter

2016 ◽  
Vol 19 (4) ◽  
pp. 944-969 ◽  
Author(s):  
Jun Zhu ◽  
Xinghui Zhong ◽  
Chi-Wang Shu ◽  
Jianxian Qiu
Keyword(s):  
Discontinuous Galerkin ◽  
Target Cell ◽  
Hyperbolic Conservation Laws ◽  
Least Square ◽  
High Order Accuracy ◽  
Hyperbolic Conservation ◽  
Contact Discontinuities ◽  
New Type ◽  
Runge Kutta ◽  
Compact Stencil

AbstractIn this paper, we propose a new type of weighted essentially non-oscillatory (WENO) limiter, which belongs to the class of Hermite WENO (HWENO) limiters, for the Runge-Kutta discontinuous Galerkin (RKDG) methods solving hyperbolic conservation laws. This new HWENO limiter is a modification of the simple WENO limiter proposed recently by Zhong and Shu [29]. Both limiters use information of the DG solutions only from the target cell and its immediate neighboring cells, thus maintaining the original compactness of the DG scheme. The goal of both limiters is to obtain high order accuracy and non-oscillatory properties simultaneously. The main novelty of the new HWENO limiter in this paper is to reconstruct the polynomial on the target cell in a least square fashion [8] while the simple WENO limiter [29] is to use the entire polynomial of the original DG solutions in the neighboring cells with an addition of a constant for conservation. The modification in this paper improves the robustness in the computation of problems with strong shocks or contact discontinuities, without changing the compact stencil of the DG scheme. Numerical results for both one and two dimensional equations including Euler equations of compressible gas dynamics are provided to illustrate the viability of this modified limiter.

scholarly journals A New Flux Splitting Scheme Based on Toro-Vazquez and HLL Schemes for the Euler Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Pascalin Tiam Kapen ◽  
Tchuen Ghislain
Keyword(s):  
Euler Equations ◽  
Compressible Flows ◽  
Arithmetic Mean ◽  
Shock Propagation ◽  
Test Cases ◽  
Splitting Scheme ◽  
Pressure System ◽  
Wave Speeds ◽  
Flux Splitting ◽  
Contact Discontinuities

This paper presents a new flux splitting scheme for the Euler equations. The proposed scheme termed TV-HLL is obtained by following the Toro-Vazquez splitting (Toro and Vázquez-Cendón, 2012) and using the HLL algorithm with modified wave speeds for the pressure system. Here, the intercell velocity for the advection system is taken as the arithmetic mean. The resulting scheme is more accurate when compared to the Toro-Vazquez schemes and also enjoys the property of recognition of contact discontinuities and shear waves. Accuracy, efficiency, and other essential features of the proposed scheme are evaluated by analyzing shock propagation behaviours for both the steady and unsteady compressible flows. The accuracy of the scheme is shown in 1D test cases designed by Toro.

Investigation of Compressor Tip Clearance Flow Based on the Discontinuous Galerkin Methods

2013 ◽  
Author(s):  
Xiaodong Ren ◽  
Chunwei Gu
Keyword(s):  
Experimental Data ◽  
High Order ◽  
Tip Clearance ◽  
High Order Accuracy ◽  
Numerical Dissipation ◽  
Order Accuracy ◽  
Tip Clearance Flow ◽  
Tip Leakage ◽  
Clearance Flow ◽  
Slope Limiter

The tip clearance flow has a significant influence on the compressor performance and stability. CFD, which is a current tool, has been widely used to investigate the flow by many researchers. In this paper, an unstructured-grid code based on a RKDG method was developed with an improved vertex-based slope limiter to ensure the nonlinear stability. The limiter tests show that the improved limiter has less numerical dissipation and it can keep the high-order accuracy. The performance for NASA Rotor 37 was simulated to validate the RKDG code. The results are compared with the experimental data and the ones computed by NUMECA FINE™/Turbo. It is shown that the results computed by the RKDG code are in better agreement with the experimental data, which implies that the high-order accuracy method is very important for improving the CFD reliability. Finally, the tip clearance flow of the compressor was investigated using the RKDG code. It is found that the tip leakage jet flow could be separated into two parts and they go downstream separately without mixing.

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